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The time table .
Connex (Veiolia) bus company has route #330 from the Central Bus Station in Ashdod to terminal 3 at Ben Gurion airport. It runs 3 times a day.
Your other options are a bus from Ashdod to the El Al Junction and then the shuttle in to the airport; or a bus to Tel Aviv and another one to the airport; or the train, which will require you to change trains in Tel Aviv.